It's good to get every piece in early so that you can get your interviews early and maybe make it in before being compared to a more competitive group that applies later on. Also, it shows your initiative and organization skills (at least that's what it would seem like to me if I were on the board, but I'm not so my thoughts won't be accurate! 😳 )
I've heard that some committees look at when the application was turned in when there are many applicants with a similar level of competitiveness. Again, I'm not sure.